[gdl]

Informal reasoning: in a=b, the 'a' and 'b' are merely placeholders that act as pointers to the same underlying value, so they can be used interchangeably. It's no different than referring to "seven" and "the integer directly following six" - I could use either reference any place I could use the other with no effect on the overall statement. Ditto for c=d. All that is happening with a+c=b+d is that two references to values are being changed to different references with the exact same underlying values, so the result is necessarily the same.

See also http://en.wikipedia.org/wiki/Peano_axioms if you prefer the math and logic jargon. High school geometry taught me to dislike dealing with formal proofs, but I think that should be about the right area to look.

[pencil]

i know even i used to hate formal proofs!!!i assumed this might have a formal proof by not knowing that this property is based on informal reasoning. (but i personally like formal proofs!!!!!)